First validation of a model-based hepatic percutaneous microwave ablation planning on a clinical dataset

A model-based planning tool, integrated in an imaging system, is envisioned for CT-guided percutaneous microwave ablation. This study aims to evaluate the biophysical model performance, by comparing its prediction retrospectively with the actual ablation ground truth from a clinical dataset in liver. The biophysical model uses a simplified formulation of heat deposition on the applicator and a heat sink related to vasculature to solve the bioheat equation. A performance metric is defined to assess how the planned ablation overlaps the actual ground truth. Results demonstrate superiority of this model prediction compared to manufacturer tabulated data and a significant influence of the vasculature cooling effect. Nevertheless, vasculature shortage due to branches occlusion and applicator misalignment due to registration error between scans affects the thermal prediction. With a more accurate vasculature segmentation, occlusion risk can be estimated, whereas branches can be used as liver landmarks to improve the registration accuracy. Overall, this study emphasizes the benefit of a model-based thermal ablation solution in better planning the ablation procedures. Contrast and registration protocols must be adapted to facilitate its integration into the clinical workflow.


Microwave ablation model for Emprint devices
The model for microwave ablation used in this work is described in Tokoutsi et al. 1 .In this supplementary information, we provide further clarification to ensure the reproducibility of the results presented in this work.The design for the Emprint ® applicator is intended to reproduce the Medtronic construction 2,3 .It includes the following components: a proximal choke antenna radiating element (which is connected through the inner feed to a tapered distal radiating section) and a cooling element surrounding the radiating section and acting as a buffer towards the tissue.Since the exact internal construction of the antenna is unknown, we tuned the assumed antenna design to reproduce the ablations reported by the manufacturer.This reverse engineering approach relies on the following tasks: • Optimization of the wave reflection coefficient, as it is commonly done for MW antennas 4,5 • Compaison between the predicted ablation and the manufacturer tabulated data under the constraint of an expected power (by also considering the efficiency that can be expected from such interstitial antennas) This provides an effective model that reproduces very well the manufacturer data sheets, although it does not necessarily capture the exact construction of the Medtronic applicator.The Specific Absorption Rate (SAR) is simplified by decoupling the thermal effect from the electromagnetic effect, according to the following equation 1, where ε and σ are respectively the tissue electrical permittivity and conductivity, depending on the spatial coordinates x, y, z, and on the temperature T .
SAR(x, y, z, T ) = SAR(x, y, z, T 0 ) f (ε(x, y, z, T ), σ (x, y, z, T )) This approach allows to effectively split the SAR into two parts.The first part SAR(x, y, z, T 0 ) mainly relates to the characteristics of antenna construction and the operating frequency, T 0 beeing the initial body temperature.The second part f (ε(x, y, z, T ), σ (x, y, z, T )) effectively models the change in SAR during ablation due to non-linear effects.For the Medtronic Emprint ® applicator, this part is further simplified into f = p σ (x,y,z,T ) σ (x,y,z,T 0 ) , by dropping the dependance on the tissue permittivity ε and by using instead a scaling factor p related to the input power, as described in Table S1.
From the SAR, the deposited heat source Q appl can be determined according to equation 2, where ρ is the tissue density.Thus, this heat source can be scaled with respect to its value at the initial body temperature T 0 in the same way as for the SAR.In Figure S1, we include a visual representation of this heat source Q appl0 = ρSAR(x, y, z, T 0 ) specific to the Medtronic Emprint applicator (single antenna), which is made available in the form of an unstructured visualization toolkit file (.vtu) and can be found in the additional information of this publication.
In Table S1, we provide specifications for the tissue properties that are included in the models of the MW antenna of the Medtronic Emprint applicator 2,3 , the SAR and the bioheat equation from Pennes et al. 6 .
The numerical solution of the resulting Partial Differential Equations (PDEs) is achieved by utilizing an in-house implementation of Finite Element (FE) approximations of the PDEs and iterative open source solvers (relying on conjugate gradient methods).In particular, for both matrix assembly and solution of the discretized linear system of equations, we rely on the Eigen library 7 .The matrix assembly exploits Eigen's vectorization capabilities, following the findings described in Rahman et al. 8 .
Another essential aspect of the Finite Element Method (FEM) implementation is the computational mesh.The domain discretization is at the moment realized using tetrahedrons generated by the mesh generator Tetgen 9 .One characteristic of the mesh generator for this application is the mesh refinement in the regions of interest, i.e. regions where the highest gradients in temperature and heat source are expected and regions where the shape of specific tissues needs to be described in detail.Hence, a two stage mesh refinement has been implemented.The initial coarse mesh is first refined according to the heat source/sink distribution.Then a second refinment step is done based on the location of the tissues of interest, e.g.segmented vasculature.
The FE discretization, the resolution of the linear system of equations, and the adaptive mesh refinement were extensively benchmarked against numerical simulations using the well established commercial solver Comsol 10 .The in-house implementation achieves performance that is appropriate for a forward planning usage in a clinical environmment.It typically computes a full simulation in less than 1 minute on a laptop with an 11th Gen Intel(R), Core(TM), i7-11850H, 2.50GHz and 32 GB RAM.This is much faster than typical computation times of generalist commercial software like Comsol 10 .

Perfusion rate in liver
A distributed temperature dependent volumetric perfusion rate (expressed in kg.m −3 .s−1 and applied to the full liver) is defined in Valvano et al. 11 and in Tsafnat et al. 12 .For a temperature of 37 • C, this volumetric perfusion rate is equal to 5 kg.m −3 .s−1 .This corresponds to the product ω b ρ b in the bioheat equation from Pennes et al. 6 , meaning that the actual perfusion rate ω b is obtained by dividing Valvano and Tsafnat values 11,12 by the blood density ρ b , resulting in a value of 0.0048 s −1 .On top of this, a perfusion sink term is applied on the subdomain defined by the segmented vasculature 13 , by enhancing the distributed perfusion rate in liver by a factor of 50 to account for the lower resistance to flow in larger vessels compared to capillary vessels.This results in a volumetric perfusion rate of 250 kg.m −3 .s−1 in the vasculature, thus an equivalent perfusion rate of 0.24 s −1 , in line with the values reported by Altrogge et al. 14 .Hence, the average perfusion rate in liver ω b can be determined according to the equation 3, where Vol liver and Vol vasc are the respective volumes of the liver and of the vasculature estimated from the segmentation tool.

Figure S1 .
Figure S1.Visual representation of the heat source Q appl0 = ρSAR(x, T 0 ) on an axis symmetric domain generated by the Medtronic Emprint applicator 2, 3 (single antenna).

Figure S2 .
Figure S2.P019 patient.Post ablation CE CT scan a and 3D visuals in b comparing ablation ground truth (in red) with predictions from the biophysical model and from manufacturer data evidence the vasculature shortage effect, with a clear stretch of the ablation ground truth towards the liver edge.Pre-and post-ablation segmented vasculatures shown in 3D visuals in c, d and e demonstrate the good performance of the registration algorithm for this specific case (matching vasculatures), resulting in a correct alignment between the ablation ground truth and the applicators.Ground truth overestimation due to the vasculature shortage remains the main artifact.

Figure S3 .
Figure S3.P007 patient.Post ablation CE CT scan a and 3D visuals in b comparing ablation ground truth (in red) with predictions from the biophysical model and from manufacturer data evidence the vasculature shortage effect, with a clear stretch of the ablation ground truth towards the liver edge.Pre-and post-ablation segmented vasculatures shown in 3D visuals in c, d and e demonstrate the good performance of the registration algorithm for this specific case (matching vasculatures), resulting in a correct alignment between the ablation ground truth and the applicators.Ground truth overestimation due to the vasculature shortage remains the main artifact.

Table S1 .
Liver tissue properties and characteristics of the MW model.

Table S2 .
Table S2 provides an overview of the average perfusion rate and of the vascular fraction per patient for the considered cohort in this study.ω b = Vol liver * ω b +Vol vasc * ω b * 50 Vol liver +Vol vasc Overview of the patient cohort used in the retrospective analysis: blood perfusion in liver